TL;DR: Google and other quantum chip makers need to search for perfect numbers as the definitive litmus test for quantum computing prowess. Perfect numbers, those rare integers equal to the sum of their proper divisors, provide a uniquely verifiable challenge that quantum computers can tackle while classical computers can double-check the results. With only 52 perfect numbers discovered so far and their fascinating binary patterns, this would create a tangible real-world benchmark everyone can understand, potentially sparking widespread excitement about math and computing. As quantum computing faces questions about practical applications, perfect number computation offers a clear, publicly verifiable demonstration of quantum advantage that could be the field's “ChatGPT moment.”
I. The Quantum Benchmark We've Been Waiting For
Remember when I wrote about perfect numbers and their weird binary sequences? I called it The Devil is in the Details, and I meant it. (https://paragraph.com/@dunsmoor.eth/devilisinthedetails)
I showed how perfect numbers follow a fascinating pattern in binary, their binary representations consist of a string of 1s followed by a string of 0s, where the number of 1s equals the Mersenne prime exponent, and the number of 0s is always one less than that exponent.
1. 6 = 110
2. 28 = 11100
3. 496 = 111110000
4. 8128 = 1111111000000
5. 33550336 = 1111111111111000000000000
6. 8589869056 = 1111111111111110000000000000000
This wasn't just mathematical trivia, it was a hint at something bigger but that’s a discussion for another time.
Now, with Google making bold claims about their quantum chip Willow solving problems "unimaginably faster" than classical computers, we need a benchmark that's both mind-blowing and verifiable. According to Google's quantum chief, their chip can solve in "about five minutes" what would take “ten septillion years” (that's 10^25 years, longer than the age of the universe) on one of the world's fastest supercomputers. (https://youtu.be/5xN8vlB2VR8)
That's a hell of a claim. But how does the average person or even most technologists verify something like that?
Enter perfect numbers. They're the technological litmus test we've been waiting for, and here's why:
II. Why Perfect Numbers Are the Perfect Test
They're mathematically rigorous: Perfect numbers have been studied since Euclid, with clear mathematical properties that can't be fudged.
They're incredibly rare: Only 52 have been discovered in 2,300+ years of mathematical exploration. Finding new ones would be a genuine achievement. (The odds of 52nd being found recent is discussed more here: The Universe Is Messing with Me, and I Can Prove It—And It Will Mess with You Too, Under Certain Conditions*, https://paragraph.com/@dunsmoor.eth/the-universe-is-messing-with-me
They're verifiable: While finding them is computationally intensive, verifying them is relatively simple – making them ideal for showcasing quantum advantage.
They follow predictable patterns: As I demonstrated in my previous work, perfect numbers follow fascinating binary patterns that suggest computational significance.
They get exponentially harder to find: Each new perfect number requires orders of magnitude more computational power, creating a perfect scaling challenge for quantum computers.
Just like those Navy pilots who described UFOs as “Tic Tacs,” we need something tangible and relatable to capture public imagination. (The Mars Tic Tac: Undeniable Evidence of Intelligence Beyond Earth, https://paragraph.com/@dunsmoor.eth/the-mars-tic-tac) The hunt for perfect numbers could be quantum computing’s “ChatGPT moment”, the point where an esoteric technology suddenly becomes tangible and exciting to the public.
III. The Quantum Advantage in Finding Perfect Numbers
Think about what Google's Willow chip claims to do – solve in minutes what would take septillions of years on classical systems. Perfect number computation fits this profile perfectly (pun absolutely intended):
Classical computers struggle increasingly with each new perfect number
The computations involve the type of massive number crunching where quantum computers theoretically excel
The binary patterns I've previously identified suggest a computation approach that aligns with quantum processing
Here's where it gets really interesting. Quantum computers excel at certain types of calculations, particularly those involving massive parallelism and probabilistic solutions. Finding Mersenne primes (which lead to perfect numbers via the formula 2^(p-1) * (2^p - 1)) requires sieving through enormous potential candidates – exactly the kind of task where quantum systems could demonstrate advantage.
The patterns I've found in the binary representation of perfect numbers and their divisors suggest there's more than just brute force at play. There's an elegant underlying mathematical structure that quantum systems might be uniquely suited to exploit.
IV. Google's Quantum Moment
Google wants to regain its edge after missing its “ChatGPT moment” in AI. Despite pioneering transformer technology in their 2017 “Attention is All You Need” paper, they watched OpenAI capture public imagination and market dominance. (https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf)
Quantum computing could be their redemption story, but only if they can demonstrate quantum advantage in ways people can understand. As that CNBC video shows, Google believes they're “about five years out from a real breakout kind of practical application.” But why wait five years when perfect numbers could provide a compelling benchmark today?
Julian Kelly, Google’s quantum leader, says they're focused on “when do we actually get to applications that can be solved on a quantum computer better than a supercomputer.” Perfect number computation fits this criteria beautifully.
V. The Verification Edge
Here’s the genius part (if I do say so myself), while quantum computers could potentially leap ahead in discovering new perfect numbers, classical computers can easily verify those discoveries. This creates an elegant validation system where:
Quantum computers race to find candidates for the 53rd and beyond perfect numbers
Classical computers verify the findings through simple divisor addition
The public gets easily digestible results: “Quantum computer X found perfect number Y, which is Z digits long”
And anyone can do it! Include the Great Internet Mersenne Prime Search (GIMPS! https://www.mersenne.org/why_join/)
This verification capability addresses one of the key challenges in quantum computing, demonstrating that the results are actually correct. As Kelly notes: “Something that's really important and that we take very seriously at Google is making sure that we kind of red team the problems that we're working on... we want to make sure that if we're making a claim that something is better on a quantum computer, we really rigorously test it.”
Perfect numbers provide exactly this kind of “red team” verification opportunity. Arguably the perfect red team because they don’t talk trash after the “win.”
VI. Beyond the Hype: Learning From AI's Trajectory
The quantum computing industry is following an eerily similar path to early AI, huge promises, technical breakthroughs hidden behind jargon, and questions about practical applications. As Nvidia's Jensen Huang said about practical quantum computing: “If you picked 20 [years], I think a whole bunch of us would believe it. Most people still think that's like a decade plus out.” (https://www.axios.com/2025/01/08/quantum-computing-stock-nvidia-jensen-huang)
But AI had its ChatGPT moment, the point where the technology suddenly became tangible and accessible. Quantum computing needs something similar.
It won’t be a consumer-friendly interface like ChatGPT, quantum computers are fundamentally different tools. But it could be a compelling, verifiable achievement that captures imagination: like discovering the next perfect number that classical computers couldn't find in the lifetime of the universe.
VII. Making Math Cool Again
There’s an overlooked benefit here too, making mathematics exciting and accessible to the public. Finding new perfect numbers through quantum computing creates a narrative bridge:
Ancient mathematics (Euclid studied perfect numbers around 300 BCE)
Modern computing challenges
Cutting-edge quantum technology
Potentially revolutionary mathematical insights
This isn’t just about quantum advantage; it’s about sparking widespread enthusiasm for mathematical exploration. It's a win-win, baby! I love those! It could be this generation’s equivalent of the excitement around the Hubble Space Telescope or the Large Hadron Collider making science and mathematics part of cultural conversation. The space race but with quantum computing and perfect numbers!
VIII. The Alien Intelligence Benchmark
Here's a cheeky thought, when we eventually find intelligent aliens (and we will), perfect numbers could be the ultimate tech-measuring contest.
Sure, they might show up with warp drives and telepathic communication, but that doesn't tell us shit about their computational capabilities. It's like comparing someone's Ferrari to your laptop, they're completely different tech domains.
"Oh, you've mastered faster-than-light travel? Cool story, bro. (To be honest anyone visiting would be far beyond us and it would be mind-blowing) But how many perfect numbers have you discovered?"
Perfect numbers could be the universal computational benchmark across the galaxy. An advanced civilization might have found the 100th or 1,000th perfect number, giving us an immediate gauge of their computational prowess. If they've discovered fewer than us, we'll know they've prioritized transportation over computation. If they've found way more, well... at least we'll know where we stand in the cosmic intelligence hierarchy.
Imagine first contact going something like this:
Alien Ambassador: "We come in peace and have traversed 47 light years to meet you."
Human Representative: "Impressive. Quick question – how many perfect numbers you've found?"
Alien Ambassador: [converts alien number system to decimal] "4.5 billion of them."
Human Representative: [whispers to aide] "Shit. Be polite."
This isn't just a joke, I mean it kind of is but it ties directly to my theory about technological determinism. As I wrote in The Mars Tic Tac, certain technologies represent unavoidable evolutionary gateways for any intelligent species. Perfect numbers computation might be one of those universal benchmarks that any advanced mathematical civilization would eventually explore making it the perfect cosmic IQ test.
IX. The Practical Path Forward
So here’s my proposal to Google, IBM, Amazon, Microsoft and other quantum players:
Adopt perfect number computation as a standard quantum benchmark so we can find who is the best in the more clear and transparent way
Create a public dashboard tracking progress toward finding the next perfect numbers
Release the binary patterns of discovered numbers to let mathematicians and computer scientists analyze them
The quantum computing race doesn't need more hype it needs tangible results that combine technical achievement with public imagination. Perfect numbers provide exactly that combination.
X. The Universe Is Rigged
I've said it before and I'll say it again, the Universe is rigged. It's rigged for those who chase dreams and do the right thing. It likes those who hustle hard and treat people with respect.
Perfect numbers aren't just mathematical curiosities they're signposts in the computational universe. Their binary patterns practically scream “there's something important here!” Their connection to quantum computing isn't coincidental it's part of the Universe showing us the path forward.
Google and other quantum pioneers have an opportunity to demonstrate quantum advantage through perfect number computation. It would showcase their technical prowess while providing a compelling narrative that captures public imagination.
The quest for perfect numbers could be quantum computing's defining moment the point where this revolutionary technology steps out of theoretical journals and into public consciousness.
So let's get those quantum bits spinning on perfect numbers. The 53rd perfect number is waiting to be found, and with it, perhaps the key to unlocking the next great leap in computational power.
After all, as I've theorized before, AI and quantum computing might just be inevitable stages in technological evolution for us and for any advanced intelligence in the universe. Finding perfect numbers could be one of the signposts showing we're on the right track.
WE. ALL. WANT. COOL. SHIT. THAT. WORKS.
Let's make quantum computing deliver exactly that.
Jonathan Dunsmoor
